Inelastic scattering results in both a loss of energy and a change in momentum, which in the case of inner shell ionisation is characteristic of the element in the sample.
Adjusting the slit to only allow electrons which have lost a specific amount of energy can be used to obtain elementally sensitive images.
The simplest method is known as the jump ratio technique, where an image recorded using electrons at the energy of the maximum of the absorption peak caused by a particular inner shell ionisation is divided by an image recorded just before the ionisation energy.
Improved elemental maps can be obtained by taking a series of images, allowing quantitative analysis and improved accuracy of mapping where more than one element is involved.
By taking a series of images, it is also possible to extract the EELS profile from particular features.